Response of a linear rectifier to signal and noise

When the input to a rectifier contains both signal and noise components, the resultant output is a complicated non-linear function of signal and noise. Given the spectra of the signal and noise input waves, the law of rectification, and the transmission characteristics of the input and output circuits of the rectifier, it should, in general, be possible to describe the spectrum of the resultant output wave. Before discussing the solution of the general problem, we shall derive some results of a simpler nature, which do not require a consideration of the distribution of the signal and noise energies as functions of frequency.